|
|
A087011
|
|
Number of primes of form 4*k+3 between n and 2n (inclusive).
|
|
3
|
|
|
0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 7, 8, 8, 7, 7, 8, 8, 7, 7, 7, 7, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
Erdős proved that between any n > 7 and its double there are always at least two primes, one of form 4*k+1 and one of form 4*k+3.
|
|
REFERENCES
|
B. Schechter, "My Brain is Open: The Mathematical Journeys of Paul Erdős," Simon & Schuster, New York, 1998, p. 62.
|
|
LINKS
|
|
|
MATHEMATICA
|
a[n_] := Module[{c = 0}, Do[If[Mod[k, 4] == 3 && PrimeQ[k], c++], {k, n, 2 n}]; c]; Array[a, 100] (* Amiram Eldar, Dec 16 2019 *)
|
|
PROG
|
(Magma) [#[p:p in PrimesInInterval(n, 2*n)| p mod 4 eq 3]:n in [1..100]]; // Marius A. Burtea, Dec 16 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|